| 1. |
- Gerdin, Markus, 1977-, et al.
(författare)
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Noise Modeling, State Estimation and System Identification in Linear Differential-Algebraic Equations
- 2004
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Ingår i: Proceedings of the 5th Conference on Computer Science and Systems Engineering. - Linköping : Linköping University Electronic Press. ; , s. 153-163
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- This paper treats how parameter estimation and Kalman filtering can be performed using a Modelica model. The procedures for doing this have been developed earlier by the authors, and are here exemplified on a physical system. It is concluded that the parameter and state estimation problems can be solved using the Modelica model, and that the parameters estimation and observer construction to a large extent could be automated with relatively small changes to a Modelica environment.
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| 2. |
- Gerdin, Markus, 1977-, et al.
(författare)
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On Parameter and State Estimation for Linear Differential-Algebraic Equations
- 2007
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Ingår i: Automatica. - Linköping : Elsevier. - 0005-1098 .- 1873-2836. ; 43:3, s. 416-425
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Tidskriftsartikel (refereegranskat)abstract
- The current demand for more complex models has initiated a shift away from state-space models towards models described by differential-algebraic equations (DAEs). These models arise as the natural product of object-oriented modeling languages, such as Modelica. However, the mathematics of DAEs is somewhat more involved than the standard state-space theory. The aim of this work is to present a well-posed description of a linear stochastic differential-algebraic equation and more importantly explain how well-posed estimation problems can be formed. We will consider both the system identification problem and the state estimation problem. Besides providing the necessary theory we will also explain how the procedures can be implemented by means of efficient numerical methods.
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| 3. |
- Gerdin, Markus, 1977-
(författare)
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Computation of a Canonical Form for Linear Differential-Algebraic Equations
- 2004
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Ingår i: Proceedings of Reglermöte 2004. - Linköping : Linköping University Electronic Press.
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- This paper describes how a commonly used canonical form for linear differential-algebraic equations can be computed using numerical software from the linear algebra package LAPACK. This makes it possible to automate for example observer construction and parameter estimation in linear models generated by a modeling language like Modelica.
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| 4. |
- Gerdin, Markus, 1977-
(författare)
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Identification and Estimation for Models Described by Differential-Algebraic Equations
- 2006
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Differential-algebraic equations (DAEs) form the natural way in which models of physical systems are delivered from an object-oriented modeling tool like Modelica. Differential-algebraic equations are also known as descriptor systems, singular systems, and implicit systems. If some constant parameters in such models are unknown, one might need to estimate them from measured data from the modeled system. This is a form of system identification called gray box identification. It may also be of interest to estimate the value of time-varying variables in the model. This is often referred to as state estimation. The objective of this work is to examine how gray box identification and estimation of time-varying variables can be performed for models described by differential-algebraic equations.If a model has external stimuli that are not measured or uncertain measurements, it is often appropriate to model this as stochastic processes. This is called noise modeling. Noise modeling is an important part of system identification and state estimation, so we examine how well-posedness of noise models for differential-algebraic equations can be characterized. For well-posed models, we then discuss how particle filters can be implemented for estimation of time-varying variables. We also discuss how constant parameters can be estimated.When estimating time-varying variables, it is of interest to examine if the problem is observable, that is, if it has a unique solution. The corresponding property when estimating constant parameters is identifiability. In this thesis, we discuss how observability and identifiability can be determined for DAEs. We propose three approaches, where one can be seen as an extension of standard methods for state-space systems based on rank tests.For linear DAEs, a more detailed analysis is performed. We use some well-known canonical forms to examine well-posedness of noise models and to implement estimation of time-varying variables and constant parameters. This includes formulation of Kalman filters for linear DAE models. To be able to implement the suggested methods, we show how the canonical forms can be computed using numerical software from the linear algebra package LAPACK.
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| 5. |
- Gerdin, Markus, 1977-
(författare)
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Local Identifiability and Observability of Nonlinear Differential-Algebraic Equations
- 2006
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Ingår i: Proceedings of the 14th IFAC Symposium on System Identification. - 9783902661029 ; , s. 802-807
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Konferensbidrag (refereegranskat)abstract
- Identifiability is important to guarantee convergence in system identification applications, and observability is important in applications such as control and diagnosis. In this paper, recent results on analysis of nonlinear differential-algebraic equations are used to derive criteria for local identifiability and local weak observability for such models. The criteria are based on rank tests. Examples show the relationship between the new criteria and standard methods for state-space systems.
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| 6. |
- Gerdin, Markus, 1977-, et al.
(författare)
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Nonlinear Stochastic Differential-Algebraic Equations with Application to Particle Filtering
- 2006
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Ingår i: Proceedings of the 45th IEEE Conference on Decision and Control. - 1424401712 ; , s. 6630-6635
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Konferensbidrag (refereegranskat)abstract
- Differential-algebraic equation (DAE) models naturally arise when modeling physical systems from first principles. To be able to use such models for state estimation procedures such as particle filtering, it is desirable to include a noise model. This paper discusses well-posedness of differential-algebraic equations with noise models, here denoted stochastic differential-algebraic equations. Since the exact conditions are rather involved, approximate implementation methods are also discussed. It is also discussed how a particle filter can be implemented for DAE models, and how the approximate implementation methods can be used for particle filtering. Finally, the particle filtering methods are exemplified by implementation of a particle filter for a DAE model.
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| 7. |
- Gerdin, Markus, 1977-, et al.
(författare)
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On Identifiability of Object-Oriented Models
- 2006
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Ingår i: Proceedings of the 14th IFAC Symposium on System Identification. - 9783902661029 ; , s. 820-825
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Konferensbidrag (refereegranskat)abstract
- When estimating unknown parameters, it is important that the model is identifiable so that the parameters can be estimated uniquely. For nonlinear differential-algebraic equation models with polynomial equations, a differential algebra approach to examine identifiability is available. This approach can be slow, so the present paper describes how this method can be modularized for object-oriented models. A characteristic set of equations is computed for components in model libraries, and stored together with the components. When an object-oriented model is built using such models, identifiability can be examined using the stored equations.
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| 8. |
- Gerdin, Markus, 1977-
(författare)
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Parameter Estimation in Linear Descriptor Systems
- 2004
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Linear descriptor systems form the natural way in which linear models of physical systems are delivered from an object-oriented modeling tool like Modelica. Linear descriptor systems are also known as linear differential-algebraic equations in the continuous-time case. If some parameters in such models are unknown, one might need to estimate them from measured data from the modeled system. This is a form of system identification called gray box identification. The objective of t his work is to examine how gray box identification can be performed for linear descriptor systems.To solve this problem, we use some well-known canonical forms to examine how to transform the descriptor systems into state-space form. In general, the input must be redefined to make the transformation into statespace form possible. To be able to implement the suggested identification methods, we examine how the transformations can be computed using numerical software from the linear algebra package LAPACK.Noise modeling is an important part of parameter estimation and system identification, so we also examine how a noise model can be added to linear descriptor systems. The result is that white noise in general cannot be added to all equations of a linear continuous-time descriptor system, since this could lead to differentiation of the noise which is not well defined. It is also noted that a Kalman filter can be implemented if the model is transformed into state-space form.We also discuss the problem of finding initial values for the paramet er search. We show how to formulate a biquadratic polynomial, that gives initial values for the parameter search when minimized.
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| 9. |
- Gerdin, Markus, 1977-, et al.
(författare)
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Parameter Estimation in Linear Differential-Algebraic Equations
- 2003
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Ingår i: Proceedings of the 13th IFAC Symposium on System Identification. - Linköping : Linköping University Electronic Press. - 9780080437095 ; , s. 1530-
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Konferensbidrag (refereegranskat)abstract
- This report describes how parameter estimation can be performed in linear DAE systems. Both time domain and frequency domain identification are examined. The results are exemplified on a small system. A potential application for the algorithms is to make parameter estimation in models generated by a modeling language like Modelica.
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| 10. |
- Gerdin, Markus, 1977-
(författare)
-
Using DAE Solvers to Examine Local Identifiability for Linear and Nonlinear Systems
- 2006
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Ingår i: Proceedings of the 14th IFAC Symposium on System Identification. - 9783902661029 ; , s. 808-813
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Konferensbidrag (refereegranskat)abstract
- If a model structure is not identifiable, then it is not possible to uniquely identify its parameters from measured data. This contribution describes how solvers for differential-algebraic equations (DAE) can be used to examine if a model structure is locally identifiable. The procedure can be applied to both linear and nonlinear systems. If a model structure is not identifiable, it is also possible to examine which functions of the parameters that are locally identifiable.
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| 11. |
- Gerdin, Markus, 1977-, et al.
(författare)
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Well-Posedness of Filtering Problems for Stochastic Linear DAE Models
- 2005
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Ingår i: Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference. - Linköping : Linköping University Electronic Press. - 0780395670 ; , s. 350-355
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Konferensbidrag (refereegranskat)abstract
- Modern modeling tools often give descriptor or DAE models, i.e., models consisting of a mixture of differential and algebraic relationships. The introduction of stochastic signals into such models in connection with filtering problems raises several questions of well-posedness. The main problem is that the system equations may contain hidden relationships affecting variables defined as white noise. The result might be that certain physical variables get infinite variance or contain formal differentiations of white noise. The paper gives conditions for well-posedness in terms of certain subspaces defined by the system matrices.
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| 12. |
- Schön, Thomas, 1977-, et al.
(författare)
-
A Modeling and Filtering Framework for Linear Differential-Algebraic Equations
- 2003
-
Ingår i: Proceedings of the 42th IEEE Conference on Decision and Control. - 0780379241 ; , s. 892-897 vol.1
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Konferensbidrag (refereegranskat)abstract
- General approaches to modeling, for instance using object-oriented software, lead to differential-algebraic equations (DAE). As the name reveals, it is a combination of differential and algebraic equations. For state estimation using observed system inputs and outputs in a stochastic framework similar to Kalman filtering, we need to augment the DAE with stochastic disturbances ("process noise"), whose covariance matrix becomes the tuning parameter. We will determine the subspace of possible causal disturbances based on the linear DAE model. This subspace determines all degrees of freedom in the filter design, and a Kalman filter algorithm is given. We illustrate the design on a system with two interconnected rotating masses.
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| 13. |
- Schön, Thomas, 1977-, et al.
(författare)
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A Modeling and Filtering Framework for Linear Implicit Systems
- 2003
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- General approaches to modeling, for instance using object-oriented software, lead to differential algebraic equations (DAE), also called implicit systems. For state estimation using observed system inputs and outputs in a stochastic framework similar to Kalman filtering, we need to augment the DAE with stochastic disturbances (process noise), whose covariance matrix becomes the tuning parameter. We will determine the subspace of possible causal disturbances based on the linear DAE model. This subspace determines all degrees of freedom in the filter design, and a Kalman filter algorithm is given.We illustrate the design on a system with two interconnected rotating masses.
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